What should I do about my mother who refuses to repent and make up the days she missed fasting in Ramadan due to menstruation in her youth, excusing herself with ignorance and the absence of someone to instruct her at that time?

A menstruating woman must make up for the fasts she missed in Ramadan, based on what was narrated from 'Aishah (may Allah be pleased with her) that they (the women) were commanded to make up for the fasts but were not commanded to make up for the prayers. The mother's ignorance of the ruling does not exempt her from making up the fasts. You must advise her and explain the Shari'ah ruling to her. If she insists (on not making them up), then there is no sin upon you.